Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States

A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5 dB ensures that errors from finite squeezing acting on encoded qubits are below the fault-tolerance threshold of known qubit-based error-correcting codes. By concatenating with one of these codes and using ancilla-based error correction, fault-tolerant measurement-based quantum computation of theoretically indefinite length is possible with finitely squeezed cluster states.Comment: (v3) consistent with published version, more accessible for general audience; (v2) condensed presentation, added references on GKP state generation and a comparison of currently achievable squeezing to the threshold; (v1) 13 pages, a few figure

Passive interferometric symmetries of multimode Gaussian pure states

As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful tools for their representation, while this work presents a useful tool for their analysis: passive interferometric (i.e., number-conserving) symmetries. Here we show that these symmetries of multimode Gaussian states simplify calculations in measurement-based quantum computing and provide constructive tools for engineering large-scale harmonic systems with specific physical properties, and we provide a general mathematical framework for deriving them. Such symmetries are generated by linear combinations of operators expressed in the Schwinger representation of U(2), called nullifiers because the Gaussian state in question is a zero eigenstate of them. This general framework is shown to have applications in the noise analysis of continuous-various cluster states and is expected to have additional applications in future work with large-scale multimode Gaussian states.Comment: v3: shorter, included additional applications, 11 pages, 7 figures. v2: minor content revisions, additional figures and explanation, 23 pages, 18 figures. v1: 22 pages, 16 figure

Temporal-mode continuous-variable cluster states using linear optics

I present an extensible experimental design for optical continuous-variable cluster states of arbitrary size using four offline (vacuum) squeezers and six beamsplitters. This method has all the advantages of a temporal-mode encoding [Phys. Rev. Lett. 104, 250503], including finite requirements for coherence and stability even as the computation length increases indefinitely, with none of the difficulty of inline squeezing. The extensibility stems from a construction based on Gaussian projected entangled pair states (GPEPS). The potential for use of this design within a fully fault tolerant model is discussed.Comment: 9 pages, 19 color figure

Sound clocks and sonic relativity

Sound propagation within certain non-relativistic condensed matter models obeys a relativistic wave equation despite such systems admitting entirely non-relativistic descriptions. A natural question that arises upon consideration of this is, "do devices exist that will experience the relativity in these systems?" We describe a thought experiment in which 'acoustic observers' possess devices called sound clocks that can be connected to form chains. Careful investigation shows that appropriately constructed chains of stationary and moving sound clocks are perceived by observers on the other chain as undergoing the relativistic phenomena of length contraction and time dilation by the Lorentz factor, with c the speed of sound. Sound clocks within moving chains actually tick less frequently than stationary ones and must be separated by a shorter distance than when stationary to satisfy simultaneity conditions. Stationary sound clocks appear to be length contracted and time dilated to moving observers due to their misunderstanding of their own state of motion with respect to the laboratory. Observers restricted to using sound clocks describe a universe kinematically consistent with the theory of special relativity, despite the preferred frame of their universe in the laboratory. Such devices show promise in further probing analogue relativity models, for example in investigating phenomena that require careful consideration of the proper time elapsed for observers.Comment: (v2) consistent with published version; (v1) 15 pages, 9 figure

Flexible quantum circuits using scalable continuous-variable cluster states

We show that measurement-based quantum computation on scalable continuous-variable (CV) cluster states admits more quantum-circuit flexibility and compactness than similar protocols for standard square-lattice CV cluster states. This advantage is a direct result of the macronode structure of these states---that is, a lattice structure in which each graph node actually consists of several physical modes. These extra modes provide additional measurement degrees of freedom at each graph location, which can be used to manipulate the flow and processing of quantum information more robustly and with additional flexibility that is not available on an ordinary lattice.Comment: (v2) consistent with published version; (v1) 11 pages (9 figures

Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb

We report the experimental realization and characterization of one 60-mode copy, and of two 30-mode copies, of a dual-rail quantum-wire cluster state in the quantum optical frequency comb of a bimodally pumped optical parametric oscillator. This is the largest entangled system ever created whose subsystems are all available simultaneously. The entanglement proceeds from the coherent concatenation of a multitude of EPR pairs by a single beam splitter, a procedure which is also a building block for the realization of hypercubic-lattice cluster states for universal quantum computing.Comment: Accepted by PRL. 5 pages, 5 figures + 14 pages, 9 figures of supplemental material. Ver3: better experimental dat

The Optical Frequency Comb as a One-Way Quantum Computer

In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done up-front when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Phys. Rev. Lett. 101, 130501 (2008).Comment: 20 pages, 8 figures. v2 corrects minor error in published versio

Acceleration-assisted entanglement harvesting and rangefinding

We study entanglement harvested from a quantum field through local interaction with Unruh-DeWitt detectors undergoing linear acceleration. The interactions allow entanglement to be swapped locally from the field to the detectors. We find an enhancement in the entanglement harvesting by two detectors with anti-parallel acceleration over those with inertial motion. This enhancement is characterized by the presence of entanglement between two detectors that would otherwise maintain a separable state in the absence of relativistic motion (with the same distance of closest approach in both cases). We also find that entanglement harvesting is degraded for two detectors undergoing parallel acceleration in the same way as for two static, comoving detectors in a de Sitter universe. This degradation is known to be different from that of two inertial detectors in a thermal bath. We comment on the physical origin of the harvested entanglement and present three methods for determining distance between two detectors using properties of the harvested entanglement. Information about the separation is stored nonlocally in the joint state of the accelerated detectors after the interaction; a single detector alone contains none. We also find an example of entanglement sudden death exhibited in parameter space.Comment: 17 pages, 6 figures. Version 2 updated to address referee comments and minor correction